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• W2247336264 abstract "We investigate dispersive estimates for the Schrodinger operator $H=-Delta +V$ with $V$ is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy obstruction, we establish the low-energy expansion $$ e^{itH}chi(H) P_{ac}(H)=O(1/(log t)) A_0+ O(1/t)A_1+O((tlog t)^{-1})A_2+ O(t^{-1}(log t)^{-2})A_3. $$ Here $A_0,A_1:L^1(mathbb R^n)to L^infty (mathbb R^n)$, while $A_2,A_3$ are operators between logarithmically weighted spaces, with $A_0,A_1,A_2$ finite rank operators, further the operators are independent of time. We show that similar expansions are valid for the solution operators to Klein-Gordon and wave equations. Finally, we show that under certain orthogonality conditions, if there is a zero energy eigenvalue one can recover the $|t|^{-2}$ bound as an operator from $L^1to L^infty$. Hence, recovering the same dispersive bound as the free evolution in spite of the zero energy eigenvalue." @default.
• W2247336264 created "2016-06-24" @default.
• W2247336264 creator A5049644755 @default.
• W2247336264 creator A5069727861 @default.
• W2247336264 date "2015-09-21" @default.
• W2247336264 modified "2023-09-27" @default.
• W2247336264 title "Decay estimates for four dimensional Schrodinger, Klein-Gordon and wave equations with obstructions at zero energy" @default.
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• W2247336264 hasPublicationYear "2015" @default.
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